Flat Earth Fallacy

I'm an accepting kind of person. I generally allow people to think what they want, believe what they want and (pretty much) say what they want, within reason. But occasionally an opinion is so far-fetched, insulting or incorrect that it debases human intelligence (all human intelligence, not just mine). And then I feel I must speak up.

One such 'opinion' is the belief in a 'flat' Earth. Although this topic has a substantial history (see for example Christine Garwood's Flat Earth: The History of an Infamous Idea), it has so far not been publicly contested in any great depth. Even Phil Plait, author of the ever-popular Bad Astronomy Blog, declined to give such a preposterous proposition any real air-time. And I don't blame him. It really is the most absurd idea. But it should be denounced, for any number of reasons.

The basic premise of the 'flat-Earth' protagonists is that ancient cultures were right, the Earth is flat, a circular disk bounded by ice mountains which is perfectly stationary while the sky rotates above it. Furthermore, the idea that the Earth is a sphere is an ominous lie spread across the millennia by an evil, secret establishment.

Hold on a minute. Before looking in detail at the 'evidence' which flat-Earthers purport to prove their case, there's an important point here. Belief in a flat-Earth isn't a 'religion' or a 'scientific discipline' - it stems from a belief that we have been lied to, in schools, in higher education, in fact everywhere. The truth is being covered up. In a word, there is a 'conspiracy' involved.

Not another one! Why is it that people, in surprisingly large numbers (across all genders, ages, races, and educational level) believe in conspiracies? Recent research by University of Miami political scientists Joseph E. Uscinski and Joseph M. Parent (see American Conspiracy Theories) showed that about a third of Americans believe the Bush administration was responsible for 9/11. There are also popular suspicions about the death of Princess Diana, about the moon landings, about Chemtrails, JFK and the list goes on and on and on. It's unnervingly common. Why are they so popular?

Uscinski and Parent define a conspiracy as a 'group acting in secret to alter institutions, usurp power, hide truth, or gain utility at the expense of the common good'. They point to Niccolò Machiavelli's edict that 'the strong desire to rule, and the weak desire not to be ruled'. So, it seems, wherever there is the possibility that power may reside away from the average citizen, there is a rife breeding ground for conspiracy theorists. As pointed out by psychology researchers at the University of London (Conspiracy Psychology), conspiracy theories often allow people to deal with feelings of powerlessness or with catastrophic events and to avoid feelings of uncertainty. And adherence to a controversial idea, however preposterous, also gives people an otherwise missing sense of self-importance. Quite possibly, many advocates actually don't believe in the conspiracy but enjoy the sense of group belonging which allows them to feel they are making an important societal contribution if they are vocal within the group. That is fine as long as no harm comes from such absurd beliefs.

But, rather than being harmless, conspiracy theories can themselves have harmful societal impacts (for example HIV and Ebola conspiracy theories have likely led to unnecessary deaths). But, conspiracy theories also undermine institutions that have no place being undermined, such as science, which is not their enemy.

We will come to this mistrust of science in a moment, but first we should address a fundamental question concerning flat-Earthers. Why would the oppressor seek to hide the shape of our home planet? Who is this oppressor anyway? Well, as you might imagine, the theorists are strangely silent on the matter. Of course, the argument is normally that if they knew who were responsible, it would no longer be a conspiracy. But familiar institutions are to blame, like NASA, who are well known for faking every photograph ever attributed to them!

But what about the reason? With other conspiracy theories, it's not difficult to suggest a potential cause - 9/11 for justifying the war on insurgency, Princess Diana because she was a threat to the establishment. But, why lie about a flat versus spherical Earth? The flat-Earthers make vague allusions to the usual shadowy world of corporations and governments, the deliberate removal of humankind's preeminence in the Universe or the evil denouncement of theism. In fact, the entire basis of their denouncement of heliocentrism is no different to the medieval abhorrence of Copernicanism. In fact, the language is strikingly similar. The conspiracy's aim, they say, is to demote humankind to a mere pawn in an uncaring Universe, to deny man's divinity and special significance, to eradicate the 'certain knowledge' that we and the place we live are the center of the Cosmos. So, even decades after the Vatican itself acquiesced to the Copernican view, the flat-Earthers are still firmly entrenched in an out-dated and irrational world model. In the words of Blackadder, 'to you... the renaissance was just something that happened to other people'.

Now, as a scientist it is hard for me to understand how anyone can imagine that science itself is a conspiracy. Am I, and my fellow scientists, not trying to understand and explain the Universe for the benefit of all humankind? Are we not driven merely by our inquiring minds to seek out answers to the mysteries of the Cosmos? The idea that we might wish to conspire against the non-scientist, to delude and mislead them, lie to them, even denounce their religious views, is alien to me and every scientist I know. In fact, it is insulting! As Charlie Brooker so eloquently puts it 'scientists are mistrusted by huge swathes of the general public, who see them as emotionless lab-coated meddlers-with-nature rather than, say, fellow human beings who've actually bothered getting off their arses to work this shit out' (Science Is Like A Good Friend).

So, why the mistrust of science? Well, perhaps because most people's interaction with science is with the 'lab-coated meddlers' of profit-seeking corporations or the warmongering agents of governments. But there is a vast gulf in incentive between the fundamental scientist and the applied technologist. And just because science has been used to genetically modify wheat, clone sheep or create devastating weapons of mass destruction, doesn't mean it is fundamentally bad or untrustworthy. It's humankind's use of that knowledge which is ofttimes suspect.

Another reason that many people distrust science is because they don't understand it. And there's no reason why they should, if they're not scientists. Many fields of science (among them cosmology and quantum physics) can appear very arcane, sometimes even counter-intuitive. If a scientist says an elementary particle doesn't exist until it is 'observed', he (or she) is not trying to be controversial, isn't inventing theories that have no basis in reality and isn't trying to hide the truth. Science is governed by its ability to predict, its testability and its repeatability. If it fails to explain an observation, is not testable or repeatable, it is thrown away or amended until it fits the real world. After all, it is only a 'description' of the world, although a fully-consistent one. If people find it difficult to understand or to accept, it is still no less a description of reality.

This truth also highlights another common fallacy of the flat-Earthers. The Flat Earth Society itself says that the simplest evidence for a flat Earth is found 'by relying on ones own senses to discern the true nature of the world around us'. Since when has the human consciousness been able to transcend the complexity and weirdness of the Universe? It doesn't, because human perception and philosophy are unreliable witnesses to reality. Science, on the other hand, is empirical and internally consistent. If our senses were our only reliable tools, quantum physics wouldn't exist, and there would be no such thing as the silicon chip! Even so, as we shall see, the flat-Earthers completely dispense with this proclaimed methodology anyway, and forthrightly discount the evidence of 'ones own senses'.

A constant niggle for many professional scientists is the common belief that science can be done effectively by the non-scientist. This isn't a case of elitism. I have no skills as an opera singer or an artist and so wouldn't insult such professionals by telling them how to sing Nessun Dorma or paint in the impressionist style. Likewise, without an in-depth scientific training, the necessary mathematical skills, the experimental experience and so on, non-scientists are not qualified to, or adept at, dissecting current scientific thought. But many people persist in assuming their arguments have a scientific footing or even that they follow the scientific method. They invariably do not. You cannot disprove a scientific fact, or body of lore, simply with words and thoughts. Evidence is not the same as gainsaying.

Now, as well as being an accepting person, I'm also a realist, so not only do I know the flat-Earth hypothesis is absolute nonsense, I also realize that no amount of sensible, reasoned discourse will turn the flat-Earther from his (or her) declared allegiance. No amount of rigorous, mathematical proof or well-attested experimentation will spark a glimmer of doubt in their mind. I could argue until I'm blue in the face, they will never accept the alternative view (which is backed up by evidence), because their faith is religious and I am obviously an evil minion of that global conspiracy.

I am fine with that. Their intransigence does not bother me in the least. I am happy for them to blunder through their misguided lives clinging to their delusions. It matters not a jot because the real world will go on acting in the way described by real science and won't change because they refuse to see the truth, and further refuse to accept that it is they, not us, who see the world incorrectly.

But that doesn't mean I won't point out their fallacies and publicly ridicule their absurd ideas. I could easily go through a list of ten or twenty so-called 'facts' which 'prove' the Earth is flat, debunking each and every one. But, frankly, I don't have to go to all that bother. All I need to do is show that any one of the flat-Earther's propositions violates reality, leads to a paradox or is inconsistent. But, just for good measure, I will now demonstrate how two flat-Earther 'facts' are false and absurd ideas and thereby prove once-and-for-all that flat-Earthers believe in total garbage.

1. The Altitude of the Celestial Pole

The position of the north celestial pole (the point on the sky to which the Earth's north pole points) lies very close to the star called Polaris. Let's imagine the coincidence is exact, just so we have something to mark the position of the pole on the sky. The same arguments will apply whether there's a star there or not.

If you stood at the Earth's north pole, Polaris would be directly over your head (astronomers would describe its 'altitude' as being 90 degrees). As you move away from the north pole, the position of Polaris changes. It changes by about 1 degree for every 111 km you travel away from the north pole. You can't refute that fact because it is easily measured and has been measured many times.

The logical explanation for this is that the Earth is a sphere. A change in one degree of Polaris' altitude corresponds to one degree in latitude. Hence, going right around the Earth means you'd complete 360 times 111 km which is about 40,000 km, the Earth's circumference. Incidentally, the fact that Polaris more-or-less marks the north celestial pole means it is extremely handy for navigation. It not only shows you where north is, it tells you your latitude on the Earth (your latitude is equal to Polaris' altitude).

For flat-Earthers, the variation in the altitude of Polaris is 'explained' differently. It lies at the point around which the sky rotates above the Earth. As you travel away from the north pole, it is just the perspective that changes its apparent position. In other words, the further away from it you go, the more its position changes. Well, we can easily test this. We know that traveling 111 km changes its position by 1 degree (do the measurement yourself if you don't believe me). Hence, by simple trigonometry, Polaris must be 6371 km above the surface of the Earth (the calculation is equivalent to calculating the Earth's radius in the spherical model). So, the flat Earth model concludes that Polaris is only 6371 km above the Earth's surface.

There's a few problems with this. Firstly, if 6371 km is the actual height of Polaris, then if you travel 6371 km from the north pole on a flat Earth, you have made an equilateral triangle and Polaris would be 45 degrees above your horizon. But, if you actually perform this experiment you will find Polaris is actually at an altitude of 32.6 degrees, not 45 degrees. And yes, the experiment has been done! So, the model's prediction is entirely wrong. Surprised?

Here's the second problem. If the change in position of all the stars is due to a perspective shift in the flat-Earth model, then their relative altitudes will also change. For example, if two stars are 1 degree apart on the sky near the zenith then if you travel sufficiently far that they appear near the horizon, they will be extremely close together (assuming they are the same 'height'). In such a flat world, the relative positions of the stars (not just their absolute positions) would change constantly depending on where you are. If the stars have different 'heights' this will still be the case but just in a more random manner. This clearly doesn't match at all what happens in the real sky. There would be no such thing as constellations, since no pattern of stars would stay the same for all observers.

The third problem? In the flat-Earth model, it is the sky that rotates above the Earth. The circumference of the flat-Earth is bounded by ice normally identified as Antarctica. If this were the case, the further away from the north pole you move, the wider the circular arcs the stars would take across the sky. At no point would they begin to circle a southern pole. But that is in fact what they do. Try telling an Australian that they don't! How do the flat-Earther's account for this? They simply adjust their model arbitrarily, as in 'there could be two virtual celestial hemispheres which overlap. One celestial hemisphere fixed at the North pole, and another at the South pole... the Earth can be flat and have two poles at the same time. A half of the celestial sphere rotates around the South pole, the other half around the North pole'. But the real sky doesn't behave like that either, does it? If we can invent anything we like to prove our theories, then of course anything is possible, even a flat Earth!

And, the fourth problem? You might even have spotted it yourself. Is Polaris, and possibly the other stars too, only 6371 km above the Earth's surface? Of course it's not, but the flat-Earther will insist it is. A discussion of how stellar distances are measured would be lengthy, and not warranted here, but those basic methods will also be denied by flat-Earthers whose only defense is that they are part of the conspiracy too! We know the distance to the Moon by laser ranging to be about 384,400 km, much further away than the flat-Earth predicts for the stars. But the Moon occults stars, not the stars the Moon, so the flat-Earth model leads to another inconsistency. And the defense will be the same - the measurement of the Moon's distance is wrong, it's just another part of the conspiracy. You see, we can believe anything we like if we are happy to dismiss any fact we wish.

This highlights very ably the difference between science and flat-Earth pseudo-science. Science will predict something based on its model of reality, then make sure that prediction is borne out by observation. Pseudo-science will draw a conclusion based on its model, then declare the conclusion proved ipso facto. No attempt is ever made to test the predictions of the model. The model can also be adjusted arbitrarily to suit the required conclusions. And this is supposed to be a more believable model than that of science! And it is also supposed to rely 'on ones own senses to discern the true nature of the world around us', even though it is completely at odds with what we see in the real world.

So there are many problems with the celestial motions predicted by flat-Earthers. And the only conclusion is that the flat-Earth hypothesis does not agree with the geometry that we actually measure on Earth. But the spherical Earth hypothesis does agree with the geometry we measure. Of course, the flat-Earthers will make all sorts of excuses for these discrepancies, but all of them represent a basic refusal to accept the facts that anyone can measure themselves. Or, even worse, they may provide an attempt at a philosophical discussion which is in effect meaningless, as in;

'If then the zenith stars of all the places on the earth, where special observations have been made, rise from the morning horizon to the zenith of an observer, and descend to the evening horizon, not in a plane of the position of such observer, but in an arc of a circle concentric with the northern centre, the earth is thereby proved to be a plane, and rotundity altogether disproved - shown, indeed, to be impossible' - from Zetetic Astronomy, Earth Not A Globe!

Such generic, worthless combinations of words (mostly attributed to the masters of dubious pseudo-science, the Victorians), are designed to sound coherent but in fact contain no logical argument, and yet are still presented as evidence in favour of flat-Earthism. They represent no scientific proof of anything other than the gullibility of those quoting them. But the protagonists still believe such random quotations disprove more than three millennia of investigative endeavour by the world's keenest intellects!

2. The Immovable Earth

Another belief of the flat-Earther is that the Earth is motionless (at the center of the Universe) and the sky (and everything else) is moving around it. The most common objection of the flat-Earther to a moving Earth is that we experience no effect of this motion, and that if the Earth were moving we would see parallax in the positions of the stars.

This is one of those cases where intuition fails us. We view the world in a very anthropocentric, egocentric way. The basic mechanics of the Universe are well understood, but they don't always agree with what we might expect the world to be like. Now, Isaac Newton didn't just pull his laws of motion out of a magician's hat. He experimented with the real world and fit his laws to what he observed. He then predicted things using these formulated laws and verified that they gave an accurate model of reality. Like all good scientists.

One of the things Newton discovered was that if an object is under constant motion (i.e. not accelerating or decelerating) it will continue to move until a force is applied. Alternatively, we can phrase this as if motion is constant there are no forces being applied. This law can easily be verified, and has been time and time again, so it is completely absurd to suggest it doesn't apply in specific cases.

So, imagine that you are inside a vehicle and you have no clues as to whether the vehicle is moving (no engine noise, vibrations or windows etc.). Could you tell you were moving? Yes, you could, but only if you were accelerating or decelerating. In that case you would feel a force. But with constant speed and direction you would feel no force at all and would not be able to tell whether you were moving or not.

The flat-Earther declares this proposition as absurd. But, a flat-Earther isn't surprised that a speeding aircraft doesn't violently jolt them from their seat, or pin them to the back of the aircraft as it moves, although he is surprised that the moving Earth doesn't do the same! He will argue that there is a fundamental difference, even though the aircraft may move at 1000 mph, the same speed as the Earth's rotation. So, the flat-Earther inside the aircraft, feeling no violent forces, should conclude that the aircraft is stationary and the Earth is moving beneath him? Yes? No, because according to him the Earth isn't moving either!

So, the assumption that a moving Earth should be somehow 'felt' by us leads to a paradox. The flat-Earther will just ignore this of course. Or say the Earth is 'different' by which they mean that different laws of physics apply to the aircraft and the Earth. Which is convenient for them but again is a good example of changing the parameter space to match your expectations or required conclusions.

What about the parallax of the stars? Some flat-Earthers will say, if the Earth rotates about the Sun, then the positions of the stars should change, but they do not. Well, in fact they do. It's actually one of the methods astronomers use to measure the distances to the stars. Observe a star position six months apart and its tiny change in location due to the Earth being on opposite sides of the Sun can tell you its distance. Parallaxes are extremely small and if you do the sums it turns out even the very nearest stars are extremely far away. Trillions of kilometers.

Other flat-Earthers will admit that stellar parallaxes exist but will declare the distances they imply as far too large to be real (notice how the flat-Earthers themselves can't agree on what is real or not). Why? Simply because it means humans aren't quite as important as they'd like to think and the Universe is much bigger than they are comfortable with. Again, the conclusion is preempted in order to fit a geocentric model. This is also convenient, of course, because the flat-Earther requires those stars to be very close; 6371 km above the Earth in the case of Polaris. But the argument is now circular because, as we've already seen, that belief results in more inconsistencies.

And this highlights another difference between science and flat-Earth pseudo-science. Science will adjust its view, re-assess its model, if facts do not agree with the current theory. Pseudo-science will ignore those facts or simply declare them inadmissible. Again, we can prove anything we like, even a flat Earth, if we are permitted to ignore the observed facts. And this is what the flat-Earthers do, over and over again.

So, is there any concrete evidence that the Earth moves? Well, yes there is. It is known as Foucault's pendulum after the French physicist who first demonstrated it. The principle is very simple. A pendulum will continue to swing in the same direction as long as no forces are applied to it. If you put a pendulum at the north pole and start it swinging you will find its orientation rotates once in exactly 24 hours (actually it rotates in one 'sidereal' day which is slightly less than 24 hours). The reason is that the Earth is spinning beneath the pendulum. If you do the same experiment at the Earth's equator, the plane of the pendulum's swing does not change relative to the Earth, as you'd expect. At intermediate latitudes the pendulum precesses more slowly than at the poles, but in a precise and predictable way dictated by the geometry of a spherical, moving Earth. Foucault's pendulum is not a 'thought experiment'. The effect has been demonstrated in the real world, even at the south pole, under stringent experimental conditions. And yes, it matches exactly what you'd predict.

Do the flat-Earthers have an explanation for this? No they don't. They just insist that the effect doesn't happen at all and cast suspicions on a technique that wasn't demonstrated until 1851, as if it matters when someone thought up the demonstration. So, again, the observational evidence is simply dismissed by flat-Earthers because it doesn't fit the flat-Earth model.

But the flat-Earther will continue to argue for a stationary Earth with statements such as 'if both the Earth and its atmosphere are spinning 1,000 mph west to east, then why don't pilots need to make 1,000 mph compensation acceleration when flying east to west?', and 'if the atmosphere is constantly being pulled along with the Earth's rotation, then why can I feel the slightest westward breeze but not the Earth's 1,000 mph eastward spin?' and 'if the Earth is spinning beneath us, why can't I just hover in a helicopter, wait until my destination reaches me, and then land when it comes?'. These statements demonstrate again a complete misunderstanding of how the Universe works, a misunderstanding born of an  anthropocentric worldview, and one that violates basic physical principles.

To the scientist there is no conundrum here at all. You see, conceptually speaking, the flat-Earther's worldview is effectively detaching objects from the Earth and placing them in another reference frame, one which is itself moving relative to the Earth. By doing this, his conclusions seem to be at odds with the idea of a moving Earth. But these objects (the atmosphere, an aircraft, a helicopter etc.) are not in their own, special reference frame, they are in the same reference frame as the Earth. There is no universal, stationary (or moving) reference frame to which you and I, or aircraft or helicopters belong.

This concept seems to be one of the most difficult for flat-Earthers to grasp, and many non-scientists too. In a world in which we are used to relating every object to our own, singular, insular reference frame, it is a conceptual leap to discover that there are in fact no universal reference frames in the Universe. It was something Isaac Newton alluded to and Albert Einstein formulated beautifully.

Perhaps the principle can best be explained by reference to forces and velocities. In order to change your velocity relative to something else, a force needs to be applied. Whilst you are standing on the Earth (or jumping above it) there is no magical force which suddenly appears and changes your motion relative to it. So, whether you want to fly your aircraft east or west you still have to apply the same force to change your speed relative to Earth. You cannot feel the atmosphere rushing past you because you are stationary relative to it. The Earth doesn't move beneath you when you jump up because you are already stationary relative to it. It's actually a very basic and simple principle. But when a flat-Earther ignores it they violate another basic principle - that you cannot create energy (or force) out of thin air!

Of course, I have addressed only two of the objections that flat-Earthers have to the idea of a spherical Earth. But I have demonstrated that both lead to inconsistencies or violate what we observe in the real world. There are many other objections; NASA have faked all their images of the Earth, gravity doesn't exist (seriously!), ships don't sink below the horizon, the Bible and the Quran both say the Earth is flat (and they should know), the tides are caused by the Earth moving up and down, that synchronous rotation of planetary Moons can't happen, that the Sun is located a few hundred miles above the Earth, that explorers who have discovered the edge of the world have been silenced, that the Moon does not reflect sunlight (it is a gigantic lamp), that we never went to the Moon (or sent space probes to the planets), that satellites don't exist, and so on and on and on and on. I don't need to address any of these (although any and all of them can be disproved easily) because the demonstration of only one inconsistency (as I've done) is enough to lay the flat-Earth hypothesis to rest.

As I said previously, the flat-Earther will dismiss every argument presented here (or elsewhere) by ignoring the facts, denying the facts, quoting ancient sources of 'erudition', quoting religious texts, or presenting pseudo-scientific or philosophical arguments with no actual content. What they never do, of course, because they can't, is provide testable, irrefutable, mathematical proof that their assertions match reality or demonstrate how the predictions of their model match reality. Nor do they ever (because they can't) provide absolute, testable, irrefutable evidence that the spherical Earth model leads to inconsistencies with the real world.

No amount of real evidence can sway the flat-Earther from their personal truth. To them, it is the same as a religious conviction; the only proof they need is the belief itself. They will not listen to reason and will always persist in the accusation that they are being lied to.

On the other hand, being a scientist, I am happy to listen to evidence for a particular world view. But I haven't heard anything yet that convinces me the Earth is flat. The onus is on the flat-Earthers to change that. So, it's over to them.